COURSE TITLE: ECE 386 Computational Electromagnetics and Photonics

CATALOG DESCRIPTION: Introduction to the finite-difference time-domain (FDTD) method in numerical modeling of electromagnetic and optical wave interactions with engineering structures. Topics: finite differences; Maxwell’s equations; numerical dispersion and stability; free-space and waveguide field sources; absorbing boundary conditions; material dispersions and nonlinearities.

REQUIRED TEXT: A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, second ed. Norwood, MA: Artech House, June 2000.

REFERENCE TEXT: A. Taflove, ed., Advances in Computational Electrodynamics: The Finite-Difference Time-Domain Method. Norwood, MA: Artech House, 1998.

COURSE COORDINATOR: Allen Taflove

COURSE GOALS: To provide the electrical engineering student with the foundation to numerically model electromagnetic wave interactions in modern high-speed electronic and optical circuits, especially >10-gigabit/sec fiber optics and VLSI-scale integrated optics.

PREREQUISITE: ECE 308 or the equivalent.

DETAILED COURSE TOPICS:

Week Lectures Topic

1 1 Introduction to contemporary problems in electromagnetic wave
engineering and techniques in computational electromagnetics.

2 Development of finite differences from Taylor series; truncation error.

3 Application of finite differences to the 1D scalar wave equation.

Assign Project 1: Simulate the 1D time-domain scalar wave equation;
investigate its numerical dispersion, stability, and accuracy properties.

2 4 Numerical dispersion of the 1D scalar wave equation.

5 Numerical stability of the 1D scalar wave equation.

6 Simple wave source and absorbing boundary conditions.

3 7 Review of Maxwell’s equations in differential and integral form;

transverse electric (TE) and transverse magnetic (TM) polarizations.

8 Introduction to Yee’s central differencing in 1-D space and time.

9 Numerical dispersion and stability of the 1D Yee algorithm; simple wave sources and absorbing boundaries.

Assign Project 2: Program the 1D Yee algorithm with simple wave- source and absorbing boundary conditions; investigate its numerical dispersion, stability, and accuracy properties.

4 10 Introduction to Yee’s central differencing in 2-D space and time.

11 Numerical dispersion and stability of the 2D Yee algorithm.

12 Zoned-grid plane-wave source in 2D.

5 13 Modal source conditions, 2-D metal waveguides.

14 Modal source conditions, 2-D dielectric waveguides.

15 Theory of analytical absorbing boundary conditions (ABC’s) in 2-D.

Assign Project 3: Program the 2D TM Yee algorithm to model a parallel-plate metal waveguide and a dielectric slab waveguide. Numerically evaluate the waveguide dispersion characteristics including modal-cutoff phenomena, group velocity, and group-velocity dispersion.

6 16 Numerical implementation of first and second-order accurate Mur

ABC’s in 2-D free space.

17 Theory of Berenger’s perfectly matched layer (PML) ABC in 2-D.

18 Numerical implementation of Berenger’s PML ABC (2D TM case), free space and waveguides.

7 19 Use of the discrete Fourier transform to obtain wideband spectral information from the impulse response.

20 Relation of time-domain and frequency-domain properties of guided waves; understanding modal cutoff, dispersion, and group-velocity dispersion.

21 Introduction to the physics of dispersive and nonlinear materials.

Assign Project 4: Program the 2D TM Yee algorithm to model the
formation of spatial optical solitons in homogeneous Kerr nonlinear
media. Investigate soliton-soliton collision interactions.

8 22 Convolutional approach to modeling dispersive materials.

23 Auxiliary differential equation modeling of dispersive materials.

24 Auxiliary differential equation modeling of nonlinear dispersive

materials.

9 25 Formation of temporal optical solitons in waveguides.

26 Formation of spatial optical solitons in homogeneous Kerr media.

27 Auxiliary differential equation modeling of optical-gain materials.

10 28 Incorporation of optical gain in simple 1-D microcavity laser

simulations.

29 Passive and active 2-D microcavity laser models.

30 Recent developments and research horizons.

COMPUTER USAGE: Four programming project assignments (see above).

LABORATORY PROJECTS: None

GRADES: No exams. Instead each student is assigned four electromagnetic wave simulation projects of progressive difficulty and sophistication weighted at 10%, 20%, 30%, and 40% of the final grade. Each project requires: (1) solution of the associated homework problems that spotlight the fundamental underlying theory; and (2) development of simulation software from the fundamental theory using Fortran, C, or C++ as selected by each student. Grading factors include assessment of student understanding of the theory, success in programming, and effectiveness in displaying the results of the simulations.

COURSE OBJECTIVES: When a student completes this course, s/he should be able to:

1) Understand the scope of contemporary and emerging application areas in electromagnetic wave technology, especially high-speed electronic and optical communications.

2) Understand the concepts and analysis approaches for numerical dispersion and stability of FDTD electromagnetic wave simulations.

3) Understand means to source waves in free space and in waveguides in numerical FDTD simulations.

4) Understand the theory and numerical implementation of widely used analytical and PML absorbing boundary conditions for FDTD grids.

5) Understand the usage and limitations of the discrete Fourier transform in obtaining wideband spectral information from calculations of the impulse response of an electromagnetic system.

6) Understand the mathematical basis and numerical modeling of frequency-dispersive and nonlinear materials in FDTD simulations.

7) Understand the formation of temporal and spatial optical solitons from the perspective of

Maxwell’s equations.

8) Construct working software that implements FDTD codes capable of solving real electromagnetic wave and optical engineering problems.

9) Begin to read the research literature in FDTD modeling for engineering electromagnetics.

ABET CONTENT CATEGORY: 100% Engineering (Design component)